{"id":96,"date":"2022-03-22T09:59:50","date_gmt":"2022-03-22T08:59:50","guid":{"rendered":"http:\/\/localhost\/hjernerehab\/?p=96"},"modified":"2022-12-04T10:31:25","modified_gmt":"2022-12-04T10:31:25","slug":"normalkurven","status":"publish","type":"post","link":"https:\/\/hjernerehab.dk\/index.php\/2022\/03\/22\/normalkurven\/","title":{"rendered":"Normalfordelingen"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">Hvis man laver et histogram over en m\u00e6ngde tilf\u00e6ldige h\u00e6ndelser, vil der fremkomme en kontur af grafikken. Er h\u00e6ndelserne fuldst\u00e6ndigt tilf\u00e6ldige, f\u00e5r man en figur, der begynder og slutter brat, og har en helt lige top, fordi alle resultaterne har samme sandsynlighed for at indtr\u00e6ffe, og man har en s\u00e5kaldt &#8216;rektangul\u00e6r fordeling&#8217;. F.eks. har lydbegrebet &#8216;hvid st\u00f8j&#8217; en rektangul\u00e6r fordeling af frekvensindhold, for alle frekvenser optr\u00e6der lige hyppigt og i samme omfang. Men rigtig ofte ligner histogrammets kontur en klokke, og s\u00e5 har man fat i en normalfordeling. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Der er flere typer fordelinger, men de er ikke relevante her. Der skelnes ogs\u00e5 mellem diskrete og kontinuerte h\u00e6ndelser, men det er heller ikke noget, vi dykker ned i.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wikipedia beskriver normalfordelingen s\u00e5ledes:<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"536\" height=\"293\" src=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Rektangulaer-fordeling.png\" alt=\"\" class=\"wp-image-1226\" srcset=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Rektangulaer-fordeling.png 536w, https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Rektangulaer-fordeling-300x164.png 300w\" sizes=\"auto, (max-width: 536px) 100vw, 536px\" \/><figcaption class=\"wp-element-caption\">Rektangul\u00e6r fordeling<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"425\" src=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Normalfordelt-histogram.png\" alt=\"\" class=\"wp-image-1227\" srcset=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Normalfordelt-histogram.png 620w, https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/12\/Normalfordelt-histogram-300x206.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><figcaption class=\"wp-element-caption\">Normalfordeling<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\" style=\"font-style:normal;font-weight:100\">&#8220;Hvad&nbsp;<em>normalt<\/em>&nbsp;er der ved normalfordelingen? Teoretisk adskiller normalfordelingen sig fra andre sandsynlighedsfordelinger ved sin rolle i den centrale gr\u00e6nsev\u00e6rdis\u00e6tning. Meget popul\u00e6rt udtrykt siger denne s\u00e6tning, at en st\u00f8rrelse der fremkommer som resultatet af mange sm\u00e5 tilf\u00e6ldige og uafh\u00e6ngige&nbsp;bidrag, vil v\u00e6re (tiln\u00e6rmelsesvis) normalfordelt. Dette giver en teoretisk &#8220;begrundelse&#8221; for hvorfor netop denne fordeling ofte er brugbar i praktiske anvendelser.&#8221; <\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Den fort\u00e6ller alts\u00e5, at hvis man har mange tilf\u00e6ldige h\u00e6ndelser (som de mange vidt forskellige individer, der kommer i en kommunes genoptr\u00e6ning) vil de v\u00e6re normalfordelt. Normalfordelingsfunktionen ligner en klokke, n\u00e5r man tegner den. Derfor kaldes den ogs\u00e5 klokkefunktionen. Den kaldes ogs\u00e5 Gaussfordelingen efter den legendariske matematiker, der kom med formlen for funktionen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Det interessante i forhold til denne side er, at den visualiserer problemet ved at bruge baggrundsviden frem for reel, nutidig og s\u00e6rligt individuel viden. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En normalfordeling kan beskrives alene med middelv\u00e6rdien (toppunktet, \u03bc), og spredningen (\u03c3). Det vil <strong>altid <\/strong>forholde sig s\u00e5dan, at 68,2 %  af tilf\u00e6ldene vil v\u00e6re inden for gennemsnittet +\/- en spredning. N\u00e6sten en tredjedel, vil falde udenfor. <\/p>\n\n\n\n<figure class=\"wp-block-image alignleft size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/04\/Normalfordelingen-2.png\" alt=\"Grafisk afbildning af normalsordelingfunktionen. \" class=\"wp-image-451\" width=\"256\" height=\"213\" srcset=\"https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/04\/Normalfordelingen-2.png 511w, https:\/\/hjernerehab.dk\/wp-content\/uploads\/2022\/04\/Normalfordelingen-2-300x250.png 300w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><figcaption class=\"wp-element-caption\">Normalfordelingingen.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Det vil alts\u00e5 betyde, at hvis der kommer tilstr\u00e6kkeligt mange ramte til et genoptr\u00e6ningssted, vil 68,2 % opf\u00f8re sig omtrent som gennemsnittet, mens resten ikke har den store effekt af genoptr\u00e6ning ud fra gennemsnitsmodellen. Dette her er et indiskutabelt matematisk faktum, uanset hvad terapeuterne og deres underviseres erfaringer bilder dem ind. Den sidste tredjedel vil v\u00e6re anderledes i deres l\u00e6ringsstil, eller deres historik, eller deres motivation, eller alle deres tabte kampe med &#8220;systemet der ved alt&#8221;, eller &#8230; De vil bare v\u00e6re anderledes nok til, at man ikke f\u00e5r et s\u00e6rligt godt resultat ud af, at g\u00f8re som man plejer. Alts\u00e5 basere sig p\u00e5 baggrundsviden fremfor reelt observeret, lyttet og m\u00e5lt viden.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Det er ikke umuligt, at kurven er meget sn\u00e6ver, dvs. lav spredning, men det ville betyde, at alle individer reagerede stort set ens (gennemsnitligt normalt) p\u00e5 terapien. Men jeg tror, at det er meget mere sandsynligt, at en tredjedel modtager en stort set nyttel\u00f8s tr\u00e6ning (og regn lige p\u00e5, hvad det koster). Det ville v\u00e6re rart, hvis en eller anden kommune har data p\u00e5 dette her, som vi kan analysere.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hvis man laver et histogram over en m\u00e6ngde tilf\u00e6ldige h\u00e6ndelser, vil der fremkomme en kontur af grafikken. Er h\u00e6ndelserne fuldst\u00e6ndigt tilf\u00e6ldige, f\u00e5r man en figur, der begynder og slutter brat, og har en helt lige top, fordi alle resultaterne har samme sandsynlighed for at indtr\u00e6ffe, og man har en s\u00e5kaldt &#8216;rektangul\u00e6r fordeling&#8217;. F.eks. har lydbegrebet [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"_themeisle_gutenberg_block_has_review":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-96","post","type-post","status-publish","format-standard","hentry","category-viden"],"_links":{"self":[{"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/posts\/96","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/comments?post=96"}],"version-history":[{"count":9,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions"}],"predecessor-version":[{"id":1238,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/posts\/96\/revisions\/1238"}],"wp:attachment":[{"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/media?parent=96"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/categories?post=96"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hjernerehab.dk\/index.php\/wp-json\/wp\/v2\/tags?post=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}